Linear Discriminant Analysis (LDA) Mathematical Intuition | Machine Learning

In this video, we will try to get the intuition behind the Linear Discriminant analysis.

If you know PCA technique for dimensionality reduction then it will be easy understand this concept.

Let us understand, what's the main difference between PCA and LDA?

PCA tries to capture the maximum variance between the new set of features developed as compared to the previous ones. 
But in LDA we try to find a separation boundary for which we try to maximize the following function:

$$J\left ( v \right ) = \frac{\left ( \mu _ 1 - \mu _ 2 \right )^2}{{s_1}^2 + {s_2}^2}$$

Where \mu _ 1 and s_1 is the mean and standard deviation of the first features and similar is the definition for \mu _ 2 and s_2.

What is Linear Discriminant Analysis (LDA)?
Linear Discriminant Analysis is a dimensionality reduction technique that is commonly used for supervised classification problems. It is used for modelling differences in groups i.e. separating two or more classes. It is used to project the features in higher dimension space into a lower dimension space. 

ML | Linear Discriminant Analysis:
https://www.geeksforgeeks.org/ml-linear-discriminant-analysis/